What is...a quotient vector space?

Goal.
Explaining basic concepts of linear algebra in an intuitive way.

This time.
What is...a quotient vector space? Or: Identifying information.

Slides.

#linearalgebra
#algebra
#mathematics

[yankeed]

Nicely done! Your “clickbait” title slide 😉 “Parallel lines are points?” zeroed in on one of the intuitively difficult aspects, at least for me, of the quotient vector space concept. I’ve read and heard many lecturers talk about “zeroing out” the vector subspace but none actually explained and demonstrated it nearly as well. The typical textbook approach of introducing the formal definitions then jumping through theorems wasn’t working for me - I kept getting stuck on “but what is going on?” Your excellent graphics and examples filled in the missing intuition that then let me grasp the more formal framework. Your analogies with information and group theory also helped me to get to “oh, I get it now”. Thanks and I’ll be investing my time to check out your library of material as I explore more topics!

[pedrocolangelo]

Sir, I was struggling so hard in my linear algebra classes and your videos saved my life from the upcoming tests.

Thank you so much for posting this content!

[vivanvasudeva]

amazing concise useful video ! I really like the concept of ‘collapsing’ a vector space onto W — its brilliant to visualise what’s actually happening

[xy]

Excellent! Btw is there any author out there who wrote/writes book the way you explain? Overview+intuition described informally then the rigorous treatment.... Let me know plz.

[karen-]

Thank you so much! This was really helpful

[rioanderson]

Great video! Thank you! "The usual yoga 😂"

[InquilineKea]

Wow, W could be kid or adult in V person, and then all kids in V / W are equal...